multiple regression

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 20 Nov 2009 12:33:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258745867db665dgoz8bq4jq.htm/, Retrieved Fri, 20 Nov 2009 20:37:59 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258745867db665dgoz8bq4jq.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Algind = algemene index Gezuitg = gezondheidsuitgaven Tijdreeksen van januari 2001 tot december 2005 met basisjaar 1996.

Dataseries X:

» Textbox « » Textfile « » CSV «

107.11 107.56 107.57 107.70 107.81 107.67 108.75 107.67 109.43 107.72 109.62 108.35 109.54 108.25 109.53 108.26 109.84 108.31 109.67 108.33 109.79 108.36 109.56 108.36 110.22 108.97 110.40 109.62 110.69 109.60 110.72 109.64 110.89 109.65 110.58 109.64 110.94 109.93 110.91 109.81 111.22 109.77 111.09 110.10 111.00 110.40 111.06 110.50 111.55 111.89 112.32 112.10 112.64 111.92 112.36 112.15 112.04 112.16 112.37 112.17 112.59 112.32 112.89 112.38 113.22 112.34 112.85 113.14 113.06 113.18 112.99 113.21 113.32 113.76 113.74 113.99 113.91 113.95 114.52 113.93 114.96 114.01 114.91 114.10 115.30 114.11 115.44 114.10 115.52 114.12 116.08 114.68 115.94 114.71 115.56 114.73 115.88 115.81 116.66 116.01 117.41 116.12 117.68 116.49 117.85 116.51 118.21 116.60 118.92 117.01 119.03 117.01 119.17 117.12 118.95 117.22 118.92 118.38 118.90 118.80

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -0.298335129214115 + 1.00996082592376X[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -0.298335129214115 3.053514 -0.0977 0.922506 0.461253 X 1.00996082592376 0.027186 37.1497 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.979626993332085 R-squared 0.959669046064861 Adjusted R-squared 0.958973684790118 F-TEST (value) 1380.10136733382 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.669834872622641 Sum Squared Residuals 26.0233678817206 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 107.11 108.333051307146 -1.22305130714556 2 107.57 108.474445822775 -0.904445822775337 3 107.81 108.444146997998 -0.634146997997608 4 108.75 108.444146997998 0.30585300200239 5 109.43 108.494645039294 0.935354960706211 6 109.62 109.130920359626 0.489079640374242 7 109.54 109.029924277033 0.510075722966614 8 109.53 109.040023885293 0.489976114707366 9 109.84 109.090521926589 0.749478073411183 10 109.67 109.110721143107 0.55927885689271 11 109.79 109.141019967885 0.648980032115 12 109.56 109.141019967885 0.418980032114996 13 110.22 109.757096071698 0.462903928301497 14 110.4 110.413570608549 -0.0135706085489491 15 110.69 110.393371392030 0.296628607969529 16 110.72 110.433769825067 0.286230174932573 17 110.89 110.443869433327 0.446130566673332 18 110.58 110.433769825067 0.146230174932572 19 110.94 110.726658464585 0.213341535414674 20 110.91 110.605463165474 0.304536834525529 21 111.22 110.565064732438 0.654935267562488 22 111.09 110.898351804992 0.191648195007652 23 111 111.201340052769 -0.201340052769492 24 111.06 111.302336135362 -0.242336135361861 25 111.55 112.706181683396 -1.1561816833959 26 112.32 112.918273456840 -0.598273456839888 27 112.64 112.736480508174 -0.0964805081736104 28 112.36 112.968771498136 -0.608771498136081 29 112.04 112.978871106395 -0.938871106395303 30 112.37 112.988970714655 -0.618970714654548 31 112.59 113.140464838543 -0.550464838543105 32 112.89 113.201062488099 -0.311062488098536 33 113.22 113.160664055062 0.0593359449384049 34 112.85 113.968632715801 -1.11863271580061 35 113.06 114.009031148838 -0.949031148837557 36 112.99 114.039329973615 -1.04932997361526 37 113.32 114.594808427873 -1.27480842787335 38 113.74 114.827099417836 -1.08709941783580 39 113.91 114.786700984799 -0.876700984798858 40 114.52 114.766501768280 -0.246501768280387 41 114.96 114.847298634354 0.112701365645711 42 114.91 114.938195108687 -0.0281951086874143 43 115.3 114.948294716947 0.351705283053343 44 115.44 114.938195108687 0.501804891312587 45 115.52 114.958394325206 0.5616056747941 46 116.08 115.523972387723 0.556027612276791 47 115.94 115.554271212501 0.385728787499091 48 115.56 115.574470429019 -0.0144704290193902 49 115.88 116.665228121017 -0.78522812101706 50 116.66 116.867220286202 -0.207220286201816 51 117.41 116.978315977053 0.43168402294657 52 117.68 117.352001482645 0.327998517354797 53 117.85 117.372200699164 0.477799300836299 54 118.21 117.463097173497 0.746902826503171 55 118.92 117.877181112126 1.04281888787442 56 119.03 117.877181112126 1.15281888787442 57 119.17 117.988276802977 1.18172319702281 58 118.95 118.089272885570 0.860727114430441 59 118.92 119.260827443641 -0.340827443641123 60 118.9 119.685010990529 -0.785010990529103 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.767618091420645 0.464763817158710 0.232381908579355 6 0.834458476092361 0.331083047815277 0.165541523907638 7 0.73786710263271 0.524265794734581 0.262132897367291 8 0.6283503484302 0.743299303139601 0.371649651569801 9 0.530722149271271 0.938555701457458 0.469277850728729 10 0.429458763221344 0.858917526442688 0.570541236778656 11 0.342588182756759 0.685176365513518 0.657411817243241 12 0.271878245170186 0.543756490340372 0.728121754829814 13 0.319545418641242 0.639090837282484 0.680454581358758 14 0.474222567883328 0.948445135766657 0.525777432116672 15 0.418514346086908 0.837028692173815 0.581485653913092 16 0.358302221326066 0.716604442652133 0.641697778673934 17 0.305333660719337 0.610667321438673 0.694666339280663 18 0.259895311877751 0.519790623755502 0.740104688122249 19 0.219272268180266 0.438544536360532 0.780727731819734 20 0.187440350493938 0.374880700987877 0.812559649506062 21 0.208017293405519 0.416034586811037 0.791982706594481 22 0.201395957574698 0.402791915149396 0.798604042425302 23 0.211211788354947 0.422423576709893 0.788788211645053 24 0.213463375174232 0.426926750348464 0.786536624825768 25 0.361312771301833 0.722625542603666 0.638687228698167 26 0.309802847439242 0.619605694878483 0.690197152560758 27 0.263112902546417 0.526225805092834 0.736887097453583 28 0.214977949241664 0.429955898483329 0.785022050758336 29 0.199368219928039 0.398736439856078 0.800631780071961 30 0.153384529823790 0.306769059647579 0.84661547017621 31 0.112872904207415 0.225745808414830 0.887127095792585 32 0.0825128811796986 0.165025762359397 0.917487118820301 33 0.077055098486733 0.154110196973466 0.922944901513267 34 0.078251254410655 0.15650250882131 0.921748745589345 35 0.0677681384745049 0.135536276949010 0.932231861525495 36 0.068478624375253 0.136957248750506 0.931521375624747 37 0.110812232934877 0.221624465869755 0.889187767065123 38 0.166217807221204 0.332435614442408 0.833782192778796 39 0.234192032058338 0.468384064116676 0.765807967941662 40 0.245021940376076 0.490043880752151 0.754978059623924 41 0.256768126883671 0.513536253767342 0.743231873116329 42 0.256594520520396 0.513189041040793 0.743405479479604 43 0.262326899526058 0.524653799052116 0.737673100473942 44 0.265372733632876 0.530745467265751 0.734627266367124 45 0.25833181742769 0.51666363485538 0.74166818257231 46 0.24316831483328 0.48633662966656 0.75683168516672 47 0.201892622042420 0.403785244084839 0.79810737795758 48 0.169517583599119 0.339035167198238 0.830482416400881 49 0.413963840459378 0.827927680918757 0.586036159540622 50 0.641705705948097 0.716588588103805 0.358294294051903 51 0.701776666953007 0.596446666093987 0.298223333046993 52 0.793722395441631 0.412555209116737 0.206277604558369 53 0.923689885151717 0.152620229696566 0.076310114848283 54 0.998776148345425 0.00244770330915038 0.00122385165457519 55 0.9962714862617 0.00745702747659842 0.00372851373829921 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0392156862745098 NOK 5% type I error level 2 0.0392156862745098 OK 10% type I error level 2 0.0392156862745098 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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